Question

Two blocks of masses M and 2M, are connected to a light spring of spring constant K that has one end fixed, the horizontal surface and the pulley are frictionless. the blocks are released from rest when the spring is not deformed. ​

Answer 1

Answer:

(A) Maximum extension in the spring is 4mg/k. (B) Maximum kinetic energy of the system is 2M2g2/k (C) Maximum energy stored in the spring is four times that of maximum kinetic energy of the system. (D) When kinetic energy of the system is maximum, energy stored in the spring is 4M2g2/k Read more on Sarthaks.com - https://www.sarthaks.com/426718/blocks-masses-connected-light-spring-spring-constant-that-has-one-end-fixed-shown-figure

Explanation:

Answer 2

Since pulley is frictionless and tension acting throughout the string is same,

Once Equillibrium is established,

                                                 Tension (T) = Weight of Block 2M

                                                                       T = 2Mg

The Net Force acting on Block M is Zero,

                                                 Tension (T) = Spring Force

                                                                      T = Kx     where x is the maximum extension in the spring.

Equating The Right Hand Sides,

                                                                   Kx = 2Mg

                                                                      x = 2Mg/K

This is the answer one gets if he follows Newton's Second Law.

But if one follows Principle of Conservation of Energy, he gets

                                                                      x = 4Mg/K

My Textbook follows the second method and the answer is found to be,

                                                                      x = 4Mg/K